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water to generate negative surface sites (>SiO
−
). They
can also gain protons to become positive sites (>SiOH
2
+
).
Putting water in contact with a fresh silica surface leads
to a slight acidification of the pore water, as shown in
Figure 1.2, which explains why silica is considered to be
an acidic rock. At the opposite end, a mineral like carbo-
nate will generate a basic pH (>7.0) in the pore water.
It follows that themineral surface chargeof silica appears
to be pH dependent. It is typically negative at near-neutral
pHvalues (pH5
interfacial electrochemistry can skip Sections 1.1.1 and
1.1.2 and can go directly to Section 1.1.3 of this chapter.
1.1.1 The case of silica
1.1.1.1 A simplified approach
Figure 1.1 sketches the surface of a silica grain coated by an
electrical double layer. When a mineral like silica is in con-
tact with water, its surface becomes charged due to chem-
ical reactions between the available surface bonding and
the pore water as shown in Figure 1.2. For instance, the
silanol groups, shown by the symbol >SiOH, of the surface
of silica (where > refers to the mineral crystalline frame-
work), behave as weak acid
8) and possibly positive or neutral for very
acidic conditions (pH <3). The simplest complexation reac-
tions at the surface of silica can be summarized as (e.g.,
Wang & Revil, 2010, and references therein)
-
base (amphoteric sites). This
means that they can lose a proton when in contact with
-
> SiOH+H
+
> SiOH
2
+
K
+
1 1
Local conductivity
σ
(
χ
)
s
Σ
Excess
conductivity
of the diffuse layer
Excess
conductivity
of the stern layer
d
Σ
σ
f
Neutral bulk pore water
x
-
+
+
Shear plane
OHP
M
+
M
+
X
-
X
-
X
-
X
-
X
-
X
-
X
-
X
-
X
-
X
-
Diffuse layer
-
M
+
-
A
-
+
M
+
Stern layer
+
-
+
+
+
+
-
-
M
+
-
-
M
+
M
+
-
-
+
-
-
-
-
-
Insulating
silica grain
+
M
+
-
-
-
-
+
M
+
A
-
+
+
+
M
+
-
+
+
M
+
+
-
-
M
+
M
+
-
+
+
A
-
+
A
-
+
+
+
-
M
+
M
+
+
M
+
-
Q
v
o-plane
d-plane
Immobile
layer
Mobile
layer
Figure 1.1
Sketch of the electrical double layer at the pore water
-
mineral interface coating a spherical grain (modified from Revil &
Florsch, 2010). The local conductivity
from the charged surface of the mineral. The pore water is
characterized by a volumetric charge density
Q
V
corresponding to the (total) charge of the diffuse layer per unit pore volume (in
coulombs (C) m
−
3
). The Stern layer is responsible for the excess surface conductivity
Σ
σ
(
χ
) depends on the local distance
χ
S
(in siemens, S) with respect to the conductivity
d
. These surface conductivities are
sometimes called specific surface conductance because of their dimension, but they are true surface conductivities. The Stern layer is
comprised between the o-plane (mineral surface) and the d-plane, which is the inner plane of the electrical diffuse layer (OHP stands for
outer Helmholtz plane). The diffuse layer extends from the d-plane into the pores. The element M
+
stands for the metal cations (e.g.,
sodium, Na
+
), while A
−
stands for the anions (e.g., chloride, Cl
−
). In the present case (negatively charged mineral surface), M
+
denotes
the counterions, while A
−
denotes the coions. The fraction of charge contained in the Stern layer with respect to the total charge of the
double layer is called the partition coefficient
f
.
of the pore water
σ
f
, while the diffuse layer is responsible for the excess surface conductivity
Σ
